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The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

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The asymptotic convexity of the negative likelihood function of GARCH models

Ip, W. and Wong, H. and Pan, J. and Li, D.F. (2006) The asymptotic convexity of the negative likelihood function of GARCH models. Computational Statistics and Data Analysis, 50 (2). pp. 311-331. ISSN 0167-9473

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Abstract

We prove the convexity of the negative likelihood function in the asymptotic sense for GARCH models. This property provides assurance for the convergence of numerical optimization algorithms for maximum likelihood estimation of GARCH. A simulation study is conducted in order to compare the performance of several different iteration algorithms. An example based on the log-returns of foreign exchange rates is also given.